Knowledge Holes in Epistemic Systems

• Knowledge Holes are structured absences in epistemic systems where concepts fail to fully bridge the gap between representation and reality.
• They manifest as ontic–epistemic mismatches, topological cavities, and dataset biases that hinder cohesive integration of knowledge.
• Addressing these holes requires targeted strategies such as concept consolidation, dataset augmentation, and improved integration protocols.

Searching arXiv for the cited works on knowledge holes and related formulations. Knowledge holes are structured absences, gaps, or misalignments in what can be known, represented, integrated, or acted upon within a given epistemic system. Across the literatures surveyed here, the term does not denote a single phenomenon. It refers, depending on context, to the ontic–epistemic gap generated by concept vagueness in science (Burlando, 2017); to homological cavities in conceptual or semantic complexes (Salnikov et al., 2018, Sizemore et al., 2017); to taxonomized deficiencies in AI datasets and model capabilities (Bajaj et al., 2020), representational failures under closed ontologies (Bacciu et al., 2024), and collateral forgetting after machine unlearning (Ko et al., 27 Oct 2025); to disparities in large collaborative knowledge ecosystems (Redi et al., 2020); to structurally unavailable ethical knowledge in software organizations (Gogoll, 27 Apr 2026); and to incompleteness in ranked online information environments (Khanna, 12 Oct 2025). Taken together, these works support a general understanding of knowledge holes as persistent deficits in coverage, integration, interpretability, or accessibility that are often structural rather than merely accidental.

1. Conceptual foundations and epistemic scope

A foundational formulation appears in "The knowledge paradox: why knowing more is knowing less" (Burlando, 2017). There, scientific knowledge is taken to be necessarily concept-mediated, and every concept about reality is held to be intrinsically vague. Because concepts discretize reality, they introduce sorites-like indeterminacy: no sharp boundary can be drawn between what does and does not fall under a concept. The resulting "Knowledge Paradox" is condensed as "If I know, then I do not know," later refined into a two-level form, "If I know$_{\text{epistemic}}$, then I do not know$_{\text{ontic}}$" (Burlando, 2017).

Within that framework, a knowledge hole is the structural gap between epistemic knowledge and ontic reality. The gap is not temporary ignorance caused by missing data. It is generated by conceptualization itself: concepts enable knowledge while simultaneously misrepresenting what they target. The paper states that "the formulation of concepts generates a gap between ontic and epistemic knowledge that cannot be amended, since any attempt at reducing this gap can only be carried out by formulating other concepts, and so on" (Burlando, 2017).

This suggests two distinct senses of knowledge holes that recur in later work. One is ontological or representational: an unavoidable misfit between symbol systems and reality. The other is organizational or empirical: a detectable region where available relations, concepts, or capabilities fail to cohere into an adequate whole. The later literatures largely operationalize the second sense, but they retain the first as a background intuition: every knowledge system has limits internal to its mode of representation.

The same paper also links the Knowledge Paradox to the sorites and liar paradoxes. Any concept is treated as soritical, and any statement about the world can be "reconducted to a liar" because the statement depends on vague concepts (Burlando, 2017). In that sense, knowledge holes are not only absences but self-undermining points in a conceptual scheme. Scientific progress then becomes cyclical: concept proliferation yields "periods of knowledge decay," while synthetic theories temporarily reduce inconsistency by compressing many concepts into fewer, more unifying ones (Burlando, 2017).

2. Topological and structural formulations

A more formal and directly operational notion appears in "Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge" (Salnikov et al., 2018). That paper replaces pairwise co-occurrence networks with simplicial complexes built from higher-order concept co-occurrences in arXiv mathematics and mathematical physics articles from 01/1994 to 03/2007. Concepts are vertices; an article containing $k$ concepts is mapped to a $(k-1)$-simplex, with only maximal simplices retained as facets (Salnikov et al., 2018).

Knowledge holes are identified with nontrivial homology classes. If concepts co-occur only in small subsets but no article jointly integrates enough of them to fill the cycle, the simplicial complex contains a homological hole. Formally, these are elements of

$$H_k(K) = \frac{\ker(\partial_k)}{\operatorname{Im}(\partial_{k+1})},$$

with Betti numbers

$$\beta_k(K) = \dim \ker(\partial_k) - \dim \operatorname{Im}(\partial_{k+1})$$

counting independent $k$-dimensional holes (Salnikov et al., 2018).

The empirical interpretation is precise. A homological hole is "a pattern of concepts that are pairwise or locally related, but where no article ties them together in a higher-order way" (Salnikov et al., 2018). Holes are ubiquitous in both $H_1$ and $H_2$, and their closure is interpreted as a sign of new knowledge creation: a hole "dies when a subset of their concepts appear in the same article" (Salnikov et al., 2018). The paper further reports a positive relation between hole dimension and time to closure, suggesting that larger holes separate more conceptually distant areas (Salnikov et al., 2018).

An analogous topological treatment of lexical development appears in "Knowledge gaps in the early growth of semantic networks" (Sizemore et al., 2017). There, words are nodes in a semantic feature network and edges denote shared semantic features. As children acquire words, a node-filtered growing graph induces a clique complex, and persistent homology tracks cavities in dimensions 1–3 (Sizemore et al., 2017). These cavities are treated as knowledge gaps in semantic space: regions where related concepts are present but an intermediate or bridging concept is absent.

The paper shows that such cavities are transient and structured rather than random. Their appearance matches a constrained null model based on fixed node affinities better than more random graph growth models (Sizemore et al., 2017). It also reports that node topological properties correlate with cavity filling better than lexical properties such as word length and frequency (Sizemore et al., 2017). A plausible implication is that knowledge holes, in both scientific and developmental settings, can be treated as mesoscale topological features of a growing conceptual system rather than merely as missing entries in a list.

Structural setting	Representation of hole	Closure event
Scientific concepts	Ontic–epistemic gap from concept vagueness	Never fully eliminable (Burlando, 2017)
Mathematical literature	Nontrivial homology class in a simplicial complex	Article integrates previously separate concepts (Salnikov et al., 2018)
Early semantic development	Persistent cavity in a clique complex of learned words	Acquisition of a bridging word (Sizemore et al., 2017)

These topological formulations differ from the epistemological one in (Burlando, 2017), but all treat holes as arising from structure: in one case conceptual mediation, in the others the combinatorics of connectivity.

3. Knowledge holes in artificial intelligence systems

In AI research, knowledge holes are frequently operationalized as measurable deficits in datasets, model capabilities, or representation languages. "Understanding Knowledge Gaps in Visual Question Answering: Implications for Gap Identification and Testing" (Bajaj et al., 2020) defines a knowledge gap as "an instance of limited or missing information or capabilities, which leads to an agent being inefficient or incapable of completing a given task." The paper focuses on local gaps in VQA and tags questions using a taxonomy of eight gap types: Attribute, Direction, Location, Material, Reasoning, Sentiment, Size, and State (Bajaj et al., 2020).

The empirical result is a strong skew in GQA. Attribute and Direction questions are common, while Reasoning, Sentiment, State, and Size are sparse (Bajaj et al., 2020). This is interpreted as a structural source of model weakness: training data underrepresent some reasoning skills, so models are likely to inherit corresponding knowledge holes. The work then proposes KG-specific seq2seq question generation to reduce this skew, with reported generation quality such as BLEU 0.75 and METEOR 0.87 for the triple-based Reasoning model (Bajaj et al., 2020). The paper stops short of retraining VQA systems end-to-end, but it provides a clear method for turning abstract holes into dataset diagnostics and targeted augmentation.

A related but more representationally focused account appears in "Handling Ontology Gaps in Semantic Parsing" (Bacciu et al., 2024). Neural semantic parsing is usually trained under a closed-ontology assumption: every utterance is presumed expressible in the model’s target meaning representation language. Ontology gaps arise when a user utterance is in scope for the task but requires symbols absent from the ontology (Bacciu et al., 2024). In such cases, no correct logical form exists within the available symbol set, yet the model is pressured to output some executable representation, yielding hallucination.

The paper introduces the Hallucination Simulation Framework, which splits ontology symbols into known and unknown sets and evaluates hallucination detection under out-of-ontology, out-of-domain, and in-ontology error conditions (Bacciu et al., 2024). Its best Hallucination Detection Model, using encoder activations plus confidence score, achieves Macro F1 of $0.701 \pm 0.030$ on out-of-ontology cases and $_{\text{ontic}}$0 on OOD cases, compared with 0.480 and 0.456 for a thresholded confidence baseline (Bacciu et al., 2024). It also improves answer accuracy on executable outputs from 93% to 97% and exact match from 85% to 95% (Bacciu et al., 2024). Here the knowledge hole is explicitly representational: the system lacks the ontology needed to encode the user’s intent.

A third AI context concerns post-training erasure. "Probing Knowledge Holes in Unlearned LLMs" (Ko et al., 27 Oct 2025) defines knowledge holes as valid benign prompts that the pretrained model answers well, the unlearned model answers poorly, and that cannot be answered from the forgetting set. These are unintended collateral losses of knowledge caused by machine unlearning (Ko et al., 27 Oct 2025). The paper proposes adjacent and latent probing, the latter via PPO-trained prompt generation. The judge score $_{\text{ontic}}$1 is used to reward prompts that induce nonsensical or irrelevant responses from the unlearned model (Ko et al., 27 Oct 2025).

The reported losses are severe. For RMU on WMDP-Bio, the latent probing set yields a post-unlearning average judge score of 1.040, with 98.7% of prompts scored 1, despite the pretrained model averaging 7.747 on the same prompts (Ko et al., 27 Oct 2025). Similar collapses are reported for GAKL, LLMU, and NPOGD on PKU-SafeRLHF, while standard benchmarks such as MT-Bench, ARC-easy, MMLU, and TruthfulQA show only modest degradation (Ko et al., 27 Oct 2025). This suggests that benchmark preservation can conceal large localized holes in benign capability space.

4. Large-scale knowledge ecosystems and information environments

At the level of collaborative knowledge infrastructures, "A Taxonomy of Knowledge Gaps for Wikimedia Projects (Second Draft)" (Redi et al., 2020) defines knowledge gaps as "disparities in content coverage or participation of a specific group of readers or contributors." It organizes the Wikimedia ecosystem into three root dimensions—Readers, Contributors, and Content—each divided into Representation and Interaction facets (Redi et al., 2020). Gap types include gender, age, geography, language, socioeconomic status, sexual orientation, cultural background, motivation, tech skills, disabilities, important topics, multimedia, structured data, and readability (Redi et al., 2020).

The paper is explicitly designed as groundwork for a knowledge gaps index. It emphasizes that quantification requires both metrics and reference baselines, and notes that even a familiar case like the content gender gap involves multiple measurement layers: selection, extent, and framing (Redi et al., 2020). Its broader contribution is to redefine knowledge holes as ecosystem-level disparities, not merely missing facts. In this view, a knowledge system can contain holes because some groups do not participate, some readers cannot access or interpret content, or some topics are underrepresented even when the platform is large and active.

A different but related large-scale environment is online search. "Knowing Unknowns in an Age of Information Overload" (Khanna, 12 Oct 2025) introduces an information completeness metric for ranked web search. For a query, the full result set is aggregated into a corpus vector

$_{\text{ontic}}$2

and cumulative information completeness at browsing depth $_{\text{ontic}}$3 is defined as

$_{\text{ontic}}$4

The metric quantifies how much of the semantic spectrum of available results is reflected in what the user has seen (Khanna, 12 Oct 2025).

Using 6.5 trillion search results from daily trends across 48 nations, the paper finds that information completeness is negatively associated with press restriction. A 1-SD increase in press restriction corresponds to a 0.28-SD decrease in completeness without region fixed effects and a 0.17-SD decrease with them (Khanna, 12 Oct 2025). Regionally, the first page of results yields about 62% completeness in North America but about 25% in the Middle East and North Africa (Khanna, 12 Oct 2025). In a U.S. experiment on the Sonder search platform, showing users completeness scores leads them to click results 6.14 ranks deeper on average and increases the completeness of clicked results by 7.6 percentage points; it also reduces fact resistance by 0.212 SD (Khanna, 12 Oct 2025). Here a knowledge hole is not falsehood but unseen semantic territory induced by ranking and bounded attention.

A related political communication perspective appears in "The Knowledge Gap in a High-Choice Media Environment: Experimental Evidence from Online Search" (Ulloa et al., 20 May 2026). This work distinguishes individual preconditions, structural features of the information environment, and topic characteristics as sources of knowledge inequalities. In a German field experiment with randomized verbal and financial encouragements to search on three policy topics, encouragement increases the likelihood of searching, but knowledge gains are concentrated among participants with higher education or higher civic knowledge (Ulloa et al., 20 May 2026). For child support, the local average treatment effect of search is about 0.25 for low education and about 0.57 for high education when the interaction is included (Ulloa et al., 20 May 2026). The implication is that high-choice, ranked environments do not eliminate knowledge holes merely by increasing access; users differ in their ability to convert exposure into understanding.

5. Organizational, ethical, and socio-technical knowledge holes

"The Ethical Knowledge Gap: Dispersed Knowledge, Sensemaking Failures, and Epistemic Dependence" (Gogoll, 27 Apr 2026) shifts the focus from content and representation to decision-making inside software organizations. It defines the ethical knowledge gap as "a structural condition in which the knowledge required for ethically informed decision-making is systematically unavailable at the point of decision, even when the organization as a whole may well possess it" (Gogoll, 27 Apr 2026).

The paper argues that three independently sufficient mechanisms produce this condition. First, ethically relevant knowledge is dispersed across roles and often tacit. Second, engineering sensemaking frames technical decisions in ways that obscure their ethical salience. Third, cross-role testimony suffers credibility attenuation, so hybrid technical-ethical judgments lose force as they travel through organizational hierarchies (Gogoll, 27 Apr 2026). The formal vocabulary distinguishes implementation facts $_{\text{ontic}}$5, contextual facts $_{\text{ontic}}$6, and ethically relevant relations $_{\text{ontic}}$7, with the gap defined at the decision level as

$_{\text{ontic}}$8

where $_{\text{ontic}}$9 is the subset of ethically relevant relations that become actionable (Gogoll, 27 Apr 2026).

This formulation is notable because it treats knowledge holes as local failures of epistemic integration rather than as missing information in the aggregate. The organization may possess the relevant pieces, yet no decision point receives them in a form that is both recognized and authoritative. The work also argues that common remedies—ethics training, codes, participatory workshops, or reporting channels—address only one layer of the problem unless they simultaneously reduce dispersal, improve ethical sensemaking, and alter credibility structures (Gogoll, 27 Apr 2026).

A plausible implication is that organizational knowledge holes are homologous to the mathematical and semantic ones discussed earlier: local connectivity exists, but no structure fills the interior. In the organizational case, the missing filler is not an article or concept but a reliable translation layer between implementation detail, contextual knowledge, and authoritative uptake.

6. Black holes, scientific frontiers, and broader significance

Some works use the language of holes more metaphorically but still in a technically structured way. "Quantization of Black Holes" (He et al., 2010) describes black holes as extreme reservoirs of missing information. In that framework, the black-hole radius, mass, area, and entropy are quantized,

$k$0

with entropy increments $k$1 (He et al., 2010). The paper interprets entropy as missing information and thereby treats the black hole as a quantized knowledge hole. This is not a theory of epistemic gaps in the usual sense, but it extends the notion of holes to thermodynamic and holographic information storage.

"The Dawn of Black Holes" (Lusso et al., 2022) uses the term in a different way: as a major unresolved gap in theoretical astrophysics. The established facts are that very massive black holes, $k$2–$k$3, already exist by $k$4–7, but their seeds and growth histories remain unknown (Lusso et al., 2022). Competing models include Pop III remnants, dense cluster channels, direct-collapse seeds, and more exotic mechanisms, with growth constrained by the Eddington timescale and radiative efficiency (Lusso et al., 2022). This is a frontier knowledge hole in the classical scientific sense: an area where observational constraints are real, theories are multiple, and no consensus synthesis yet closes the gap.

Across these domains, several recurrent themes emerge. First, many knowledge holes are structural and not simply remediable by adding more data. Second, holes are often revealed only when one moves beyond pairwise or benchmark-level summaries and examines higher-order connectivity, representational limits, or localized failures. Third, closure is partial and domain-specific. In mathematics a hole may die when a new article unifies concepts (Salnikov et al., 2018); in semantic development when a bridging word is learned (Sizemore et al., 2017); in VQA when data coverage is rebalanced (Bajaj et al., 2020); in semantic parsing when the system learns to abstain on ontology gaps (Bacciu et al., 2024). By contrast, in the Knowledge Paradox the ontic–epistemic gap is permanent (Burlando, 2017).

A common misconception is that knowledge holes are simply unknown facts waiting to be filled. The surveyed work indicates a more complex picture. Holes may be disparities in participation and representation (Redi et al., 2020), regions of low topological connectivity (Salnikov et al., 2018), missing competencies induced by training distributions (Bajaj et al., 2020), unseen portions of ranked information spaces (Khanna, 12 Oct 2025), local organizational failures of epistemic integration (Gogoll, 27 Apr 2026), or unavoidable limits of concept-mediated knowledge (Burlando, 2017). What unifies them is not their object but their structure: each marks a place where available elements fail to produce a complete, integrated, or actionable form of knowing.